There was some tentative interest from various Championship clubs such as Swansea City and Nottingham Foresst, but both sides have now been pipped to the signing by Rosenborg, who's Liverpool links may have proved crucial.
Liverpool could look for a buy-back clause to be included in the deal.
Earlier this month, The Mirror claimed that Liverpool were willing to offload Chirivella in the summer transfer window.
The 21-year-old has been involved in Liverpool's pre-season campaign and came on against Manchester United in the 4-1 victory for Klopp's side in front of a crowd of more than 100,000 people in MI at the weekend.
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Liverpool have accepted an initial £2.4m bid from Norwegian outfit Rosenborg for Spanish youngster Pedro Chirivella.
The midfielder has not made enough of an impression on Jurgen Klopp to force himself into his first-team plans, leading to this move away from the club on a permanent basis.